- Conference on Automorphic forms and integrable systems, Mathematical Center of Sirius University, Sochi, Feb 2020
- IMS Meeting, Galway, September 2019
- Research Seminar, SUSTech, Shenzhen, April 2019
- IQF Meeting, DCU, May 2018
- Periods in Number Theory, Algebraic Geometry and Physics, HIM Bonn, Feb 2018 [Lecture Notes]

Hi, thanks for stopping by. I am a mathematician working on the interface of physics and mathematics. I graduated in mathematics (Leipzig) and hold a PhD in both disciplines. Currently I am a Research Fellow at TCD and a Research Associate at DIAS.

My research is dedicated to an improved mathematical understanding of quantum field theory, more specifically rational CFTs.

My work makes a new start by exploring an alternative to the VOA formalism. The objects I deal with are automorphic forms on compact Riemann surfaces, with emphasis on equal treatment of genus one and higher genus (at least for the hyperelliptic case). The basic object is the partition function Z, which is a map from the Riemannian metrics to the positive real numbers. According to Einstein, the Virosoro N-point function is the N

^{th}functional derivative of Z w.r.t. the metric at N points. Nahm suggests that all correlation functions are obtained this way. Thus every chargeless field generates a continuous deformation of the manifold which induces a local change of the metric, just as attaching a handle locally distorts distances (here the continuous parameter measures the collar width). Most of my explicit results so far have been obtained for the (2,5) minimal model (Yang-Lee model). It is well-known that for genus one the partition function is given by the pair of Rogers-Ramanujan functions. We have established a system of five first order ODEs for the corresponding automorphic forms in genus two [arXiv:1705.07627], whose solutions are expected to be standard Siegel modular forms. I also established expansions in the above mentioned deformation parameter for the genus two zero-point functions obtained by gluing two tori together [arXiv:1801.08387]. In addition to the four solutions obtained from all possible pairings of the Rogers-Ramanujan functions, there is a fifth solution related to a non-holomorphic field of weight -1/5, for which I derived a separate third order ODE. Both approaches continue to work for higher genus, with the respective number of ODEs running through the Fibonacci numbers.

More recently I have investigated algebraic and convolution properties of quasi-elliptic functions [arXiv:1908.11815]. This topic arose in the computation of genus one Virasoro correlation functions but turned out to be potentially useful for calculating elliptic Feynman integrals.

My project Higher Genus Automorphic Forms in CFT is funded by an IRC Government of Ireland Postdoctoral Fellowship 2018-2020 .